Final answer:
The burglars returned to the DNC headquarters to fix improperly placed phone taps from an earlier break-in, part of a larger operation approved by President Nixon and his advisors to disrupt political opponents.
Step-by-step explanation:
The burglars broke in a second time to the Democratic National Committee Headquarters because the initial break-in's objective to wiretap DNC telephones was not accomplished successfully; the phone taps were improperly placed. This necessitated a subsequent entry to fix the issue. The burglaries were part of a series of illegal activities directed by the Committee to Reelect the President (CREEP), with involvement from high-ranking officials including President Nixon himself, to undermine political opponents. Despite initial attempts to cover up the involvement of Nixon and his advisors, the Watergate scandal unraveled, leading to indictments, resignations, and ultimately Nixon's resignation.